JP-2008-101626A shows an exhaust gas recirculation (EGR) system in which quantity of recirculation gas is controlled by an exhaust gas recirculation valve (EGR valve). In this EGR system, the quantity of exhaust gas passing through the EGR valve is computed by means of an EGR valve model which simulates a behavior of the recirculated exhaust gas passing through the EGR valve. When the engine is stably running, it is deemed that the quantity of the exhaust gas passing through the EGR valve is equal to the quantity of the exhaust gas flowing into a cylinder. When the engine is in a transitional running condition, the quantity of the exhaust gas flowing into the cylinder is computed based on the quantity of the exhaust gas passing through the EGR valve by means of a EGR diffusion model (time delay+first order lag) which simulates a behavior of the exhaust gas flowing in an intake pipe toward an intake port of the engine.
In order to improve fuel economy of the engine equipped with an EGR system, it is necessary to control the quantity of the recirculated exhaust gas flowing into a cylinder so that gas including exhaust gas is efficiently combusted in a cylinder. Thus, it is necessary to estimate the quantity recirculated exhaust gas flowing into the cylinder with high accuracy. However, in the above EGR system, an estimating accuracy of the quantity of the recirculated exhaust gas does no satisfy a required accuracy to improve a fuel economy. Especially, when the engine is in a transitional running condition, an estimation error exceeds an allowable error range.